Numerical computation of nonlinear oscillatory two‐immiscible magnetohydrodynamic flow in dual porous media system: FTCS and FEM study

Abstract

The transient Hartmann magnetohydrodynamic flow of two immiscible fluids flowing through a horizontal channel containing two porous media with oscillating lateral wall mass flux is studied. A two‐dimensional spatial model is developed for two fluids, one of which is electrically conducting and the other is electrically insulating. Both the fluid regimes are driven by a common pressure gradient. A Darcy‐Forchheimer drag force model is used to simulate the porous media effects on the flow in both the fluid regimes. Special boundary conditions are imposed at the interface. The governing second‐order nonlinear partial differential dimensionless equations are obtained for each region using a set of transformations. The resulting transport equations are controlled by the Hartmann hydromagnetic parameter (Ha), viscosity ratio parameter (α), two Darcy numbers (Da 1 and Da 2), two Forchheimer numbers (Fs 1 and Fs 2), two Reynolds numbers (Re 1 and Re 2), frequency parameter ( εA) associated with the transpiration (lateral wall flux) velocity and a periodic frequency parameter ( ω*t*). Numerical forward time/central space finite‐difference solutions are obtained for a wide range of the governing parameters. Bench marking is performed with a Galerkin finite‐element method (MAGNETO‐FEM), and the results are found to be in excellent agreement. Applications of the model include magnetic cleanup operations in coastal/ocean seabed oil spills and electromagnetic purification of petroleum reservoir fluids.

Computational simulations of hybrid mediated nano- hemodynamics (Ag-Au/Blood) through an irregular symmetric stenosis

“…These values confirm the stability and convergence of this scheme, as also verified in Hoffmann [28]. The FTCS code has been extensively validated and implemented in numerous previous simulations, including solar energy radiative heat transfer flows [29], periodic hydromagnetic flows in geophysics [30], viscoelastic blood flow with body acceleration [31], peristaltic gastro-intestinal pumping [32], thermosolutal Cross fluid blood flow in tapered arteries [33] and non-Newtonian coating hydromechanics [34]. Confidence is, therefore, justifiably high in the FTCS scheme.…”

Numerical simulation of the transport of nanoparticles as drug carriers in hydromagnetic blood flow through a diseased artery with vessel wall permeability and rheological effects

“…For computations with the FTCS code, the default values of various parameters which are used are documented in Table 3. These values are consistent with actual clinical scenarios and have been extracted from a number of previous studies [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. The species (solutal) Grashof number, GrN is not varied (concentration differences of nanoparticles within blood increases the species buoyancy force, although this is not plotted).…”

“…These values confirm the stability and convergence of this scheme as documented in Hoffmann's book [37]. The FTCS code has been extensively validated and implemented in numerous previous simulations including solar energy radiative heat transfer flows [40], periodic hydromagnetic flows in geophysics [41], viscoelastic blood flow with body acceleration [42], peristaltic gastro-intestinal pumping [43], thermosolutal cross fluid blood flow in tapered arteries [44] and non-Newtonian coating hydromechanics [45].…”

Unsteady hybrid nanoparticle-mediated magneto-hemodynamics and heat transfer through an overlapped stenotic artery: Biomedical drug delivery simulation

“…These values confirm the stability and convergence of this scheme as verified in Hoffmann [36]. The FTCS code has been extensively validated and implemented in numerous previous simulations including solar energy radiative heat transfer flows [37], oscillatory hydromagnetic flows in geophysics (MHD-assisted oil spill cleanup) [38], viscoelastic blood flow with body acceleration [39], peristaltic gastro-intestinal pumping [40], thermosolutal Cross fluid rheo-hemodynamics in tapered arteries [41] and non-Newtonian coating hydromechanics [42]. FTCS is therefore very adaptable and offers excellent accuracy in magneto-nano-hemodynamics simulation, as confirmed in the next section.…”